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  <h1 class="w3-xxxlarge">Group Explorer 3.0 Help: Group Explorer Terminology</h1>
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                <h3>Contents</h3>
                <ul>
                
                    <li><a style="text-decoration: none;"
                          href="#author-of-a-group">Author of a group</a></li>
                
                    <li><a style="text-decoration: none;"
                          href="#date-of-last-modification-for-a-group">Date of last modification for a group</a></li>
                
                    <li><a style="text-decoration: none;"
                          href="#url-of-a-group">URL of a group</a></li>
                
                    <li><a style="text-decoration: none;"
                          href="#naming-scheme-for-group-elements">Naming scheme (for group elements)</a></li>
                
                    <li><a style="text-decoration: none;"
                          href="#representation-of-a-group">Representation of a group</a></li>
                
                    <li><a style="text-decoration: none;"
                          href="#sheets">Sheets</a></li>
                
                    <li><a style="text-decoration: none;"
                          href="#visualizers">Visualizers</a></li>
                
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            <p>This page is a dictionary of terms specific to <em>Group Explorer.</em> Many other
pages in the <em>Group Explorer</em> help link here to define terms. Unlike <a href="../rf-groupterms/">the
group theory terminology page</a>, these terms are not
well-known mathematical terms; they&rsquo;re used only in <em>Group Explorer.</em></p>
<h3 id="author-of-a-group">Author of a group</h3>
<p>The files which store group information are called group files, and they can
contain information about the original author of the file. This person
encoded the description of a finite group into <em>Group Explorer&rsquo;s</em> group
definition syntax so that <em>Group Explorer</em> could load and manipulate the
group. See also <a href="#url-of-a-group">URL of a group</a>.</p>
<h3 id="date-of-last-modification-for-a-group">Date of last modification for a group</h3>
<p>The date of last modification of a group actually refers to the date on
which the file from which the group was loaded was last modified. See also
<a href="#url-of-a-group">URL of a group</a>.</p>
<h3 id="url-of-a-group">URL of a group</h3>
<p>Groups are stored on the <em>Group Explorer</em> website in files that end in the
extension <code>.group</code>. The group&rsquo;s URL is the web address (beginning with
<code>http://</code>) pointing to the <code>.group</code> file from which the group was loaded on
<em>Group Explorer&rsquo;s</em> website. Example:</p>
<p><code>https://nathancarter.github.io/group-explorer/GroupInfo.html?groupURL=groups/Z_2 x Z_4.group</code></p>
<h3 id="naming-scheme-for-group-elements">Naming scheme (for group elements)</h3>
<p>See <a href="#representation-of-a-group">representation of a group</a>.</p>
<h3 id="representation-of-a-group">Representation of a group</h3>
<p>In order to display the elements of a group on the screen, <em>Group Explorer</em>
needs to know their names. Although internally, <em>Group Explorer</em> stores
groups in a manner consistent with the mathematical abstractions that they
are, users prefer a prettier format. Each group file defines at least one
representation, or naming scheme&ndash;that is, a list of names, one for each
element of the group. Users can add additional representations (also called
naming schemes) by using the controls in <a href="../rf-um-groupwindow/">the group info
page</a>.</p>
<p>Note that group elements&rsquo; representations should not be confused with group
presentations, which are embeddings of arbitrary groups into groups of
matrices. <em>Group Explorer</em> does not currently have any features related to
group presentations.</p>
<h3 id="sheets">Sheets</h3>
<p>Sheets are a blank canvas on which the user can drop illustrations of a
group, homomorphisms to connect them, and pieces of text for description.
Thus groups need not be examined only in isolation; they can be compared to
other groups.</p>
<p>To open a new sheet, from <a href="../rf-um-mainwindow/">the main page</a>, click the
sheet icon on the top right. For more information, see <a href="../tu-sheets/">the introduction to
sheets</a> or the <a href="../rf-um-sheetwindow/">reference documentation on the sheet
interface</a>.</p>
<h3 id="visualizers">Visualizers</h3>
<p><em>Group Explorer</em> uses the term visualizer to describe any of the various
mechanisms for obtaining pictures of a group. For instance, one way to
visualize a group is through its multiplication table, so we refer to
multiplication tables as &ldquo;visualizers.&rdquo; <em>Group Explorer</em> contains four
types of visualizers: <a href="../rf-groupterms/#multiplication-table">multiplication
tables</a>, <a href="../rf-groupterms/#cycle-graph">cycle
graphs</a>, <a href="../rf-groupterms/#cayley-diagrams">cayley
diagrams</a>, and <a href="../rf-groupterms/#objects-of-symmetry">objects of
symmetry</a>.</p>
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